Improved Performance of High Areal Density Indirect
Drive Implosions at the National Ignition Facility using a
Four-Shock Adiabat Shaped Drive
The MIT Faculty has made this article openly available. Please share
how this access benefits you. Your story matters.
Citation
Casey, D.T., J.L. Milovich, V.A. Smalyuk, D.S. Clark, H.F.
Robey, A. Pak, A.G. MacPhee, et al. “Improved Performance of
High Areal Density Indirect Drive Implosions at the National
Ignition Facility Using a Four-Shock Adiabat Shaped Drive.”
Physical Review Letters 115, no. 10 (September 1, 2015). ©
2015 American Physical Society
As Published
http://dx.doi.org/10.1103/PhysRevLett.115.105001
Publisher
American Physical Society
Version
Final published version
Accessed
Thu May 26 01:13:46 EDT 2016
Citable Link
http://hdl.handle.net/1721.1/98348
Terms of Use
Article is made available in accordance with the publisher's policy
and may be subject to US copyright law. Please refer to the
publisher's site for terms of use.
Detailed Terms
PRL 115, 105001 (2015)
week ending
4 SEPTEMBER 2015
PHYSICAL REVIEW LETTERS
Improved Performance of High Areal Density Indirect Drive Implosions at the National
Ignition Facility using a Four-Shock Adiabat Shaped Drive
D. T. Casey,1 J. L. Milovich,1 V. A. Smalyuk,1 D. S. Clark,1 H. F. Robey,1 A. Pak,1 A. G. MacPhee,1 K. L. Baker,1
C. R. Weber,1 T. Ma,1 H.-S. Park,1 T. Döppner,1 D. A. Callahan,1 S. W. Haan,1 P. K. Patel,1 J. L. Peterson,1 D. Hoover,2
A. Nikroo,2 C. B. Yeamans,1 F. E. Merrill,3 P. L. Volegov,3 D. N. Fittinghoff,3 G. P. Grim,3 M. J. Edwards,1 O. L. Landen,1
K. N. Lafortune,1 B. J. MacGowan,1 C. C. Widmayer,1 D. B. Sayre,1 R. Hatarik,1 E. J. Bond,1 S. R. Nagel,1 L. R. Benedetti,1
N. Izumi,1 S. Khan,1 B. Bachmann,1 B. K. Spears,1 C. J. Cerjan,1 M. Gatu Johnson,4 and J. A. Frenje4
1
Lawrence Livermore National Laboratory, Livermore, California 94550, USA
2
General Atomics, San Diego, California 92121, USA
3
Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
4
Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
(Received 22 April 2015; published 1 September 2015)
Hydrodynamic instabilities can cause capsule defects and other perturbations to grow and degrade
implosion performance in ignition experiments at the National Ignition Facility (NIF). Here, we show the
first experimental demonstration that a strong unsupported first shock in indirect drive implosions at the
NIF reduces ablation front instability growth leading to a 3 to 10 times higher yield with fuel
ρR > 1 g=cm2 . This work shows the importance of ablation front instability growth during the National
Ignition Campaign and may provide a path to improved performance at the high compression necessary for
ignition.
DOI: 10.1103/PhysRevLett.115.105001
PACS numbers: 52.57.Fg
In inertial confinement fusion (ICF) experiments performed at the National Ignition Facility (NIF) [1], capsules
of deuterium and tritium fuel are imploded to high densities
and temperatures to initiate alpha-particle self-heating and
fusion burn [2,3]. The indirect drive ICF concept uses a
laser to irradiate a high-Z cylindrical hohlraum, which
produces a nearly uniform, thermal, x-ray drive. The x-ray
drive then ablates an outer capsule shell imploding the
remaining cryogenically frozen DT shell-mass inward. To
achieve ignition, the DT hot spot must have high enough
energy-density confined for adequate time to spark hot spot
self-heating and start a burn wave through the dense DT
shell. This requirement can be equivalently expressed as a
condition of Pτ, where P is the hot spot pressure, a measure
of the energy density, and τ is the confinement time of that
energy [4]. It has been shown [5] that P is related to the
implosion velocity (v) by balancing the hotpot internal
energy to the shell kinetic energy via 2πPR3 ∼ ϵ 12 Mv2 ,
where R is the radius of the hot spot, ϵ is the fraction of the
shell kinetic energy converted to hot spot energy, and M is
the mass of the shell. The hot p
spot
confinement
time is
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
ffi
related to the shell inertia as τ ∼ M=4πPR, and combining with the previous expression shows that Pτ ∼ ϵ1=2 vρR
[5], where ρR is the areal density. This means that a
successful ignition experiment must simultaneously
achieve efficient coupling of the shell kinetic energy to
the hot spot, high v, and high ρR.
Achieving high implosion v and high ρR is challenging
as the implosion process is subject to the Rayleigh-Taylor
(RT) instability [6–8], which becomes more virulent with
0031-9007=15=115(10)=105001(5)
the higher accelerations required to get high v and with the
steeper density gradients and higher convergences inherent
for higher ρR. Experiments during the National Ignition
Campaign (NIC) [9–13] were thought to have been
degraded by both instability growth and in the most severe
cases mix of plastic ablator material into the hot spot as a
consequence of that growth. Subsequent experiments
deliberately increased the adiabat (α) or entropy delivered
to the DT shell, by increasing the laser foot (called high
foot) to improve stability and performance [14–16]. Here, α
is defined as α ¼ P=Pcold , where Pcold is the minimum
pressure at 1000 g=cc from the DT EOS [17]. Increasing
the α is one path to reduced ablation front hydrodynamic
instability growth, and a hypothesis is that the reduced
growth [18] led directly to improved performance demonstrated by the high-foot experiments [16]. The increased α
is also predicted to lead to lower convergence, ρR, and
yields in 1D simulations. In turn, reduced convergence
leads to both reduced RT and Bell-Plesset growth [19] of
instabilities at the ice-ablator interface and the ice-gas
interface and a reduction in their perturbative impact even
for fixed final amplitude. Additionally, Dittrich et al. [14]
hypothesized that an increased foot level would reduce the
ablation front physics sensitivity to uncertainties in the
partially ionized ablated carbon. These multiple hypotheses
left the role of ablation front growth during the NIC
ambiguous.
To address the role of ablation front growth, a new laser
pulse was designed by Milovich et al. [20] to produce the
radiation drive proposed by Clark et al. [21] aimed at
105001-1
© 2015 American Physical Society
PRL 115, 105001 (2015)
PHYSICAL REVIEW LETTERS
combining the best features of both the high ρR low-foot
(LF) and improved stability high-foot (HF) drives. This
new laser pulse shape launches a stronger first shock using
a higher energy picket [see Fig. 1(a)] but with a standard
low-foot trough so that the first shock decays as it traverses
the ablator, weakening to comparable velocity to the LF
implosion when it hits the DT ice, thus maintaining a
low fuel adiabat [23]. The longer picket in this new
“adiabat-shaping” (AS) pulse launches a first shock similar
to that of HF, but with lower laser power and lower risk of
laser-plasma instabilities during the picket. The approach is
similar to the AS [24–28] techniques previously fielded in
direct drive implosions [29–31]. In this case, however, the
stability benefits are a consequence of the RichtmyerMeshkov (RM) oscillations [32–35] during the shock
transit phase, rather than a reduction of the RT growth
rate directly [21]. That is, the ablation front RM oscillation
occurs faster with the higher picket, moving the node in the
growth factor spectrum to lower mode numbers, reducing
the peak growth amplitude [see Fig. 1(b)]. X-ray radiography measurements of imposed sinusoidal modulations
confirmed [36] that indeed the peak ablation front growth
factor was reduced by moving an RM node closer to the
peak of the RT growth factor using this drive as predicted
by Clark et al. [21].
In this Letter, we show for the first time that this new
pulse shape leads to significantly higher implosion performance at high ρR. These results suggest a dominant role of
ablation front growth as a degradation mechanism of
implosion performance during the NIC (even without the
observation of ablator mix). This is accomplished by
changing the ablation front growth characteristics, while
achieving the same convergence and areal density. More
importantly, these results may provide a viable path toward
FIG. 1 (color online). (a) Laser pulse shape for the low adiabat
or low foot (blue curve), the high adiabat or high foot (red), and
the adiabat shaped (purple) drives. The high-power feature for the
first ∼3 ns is called the picket, and the trough is the following
segment at low power. Features following the trough launch
additional shocks, three shocks total for HF, and four shocks total
for AS and LF. (b) Ablation front growth factors for the LF (blue),
AS (purple), and HF (red) simulated using the code HYDRA [22].
week ending
4 SEPTEMBER 2015
high performance implosions at the high areal densities
required for ignition.
A similar concept derived from the three-shock HF
platform was to lower the trough below that of the LF
pulse [37], allowing the first shock to weaken before it hits
the DT ice [23], modestly reducing the adiabat (∼10%).
The details and results of this three-shock AS are described
by Smalyuk et al. [38]. However, the three-shock AS
represents a relatively small change in adiabat from the HF
design, while the four-shock AS results described herein (at
significantly lower adiabat than HF) are derived from the
LF platform and therefore can be more directly related to
the performance of the NIC. It is also possible, in principle,
to achieve higher ρR, higher hot spot pressure, and higher
simulated 1D performance, with this four-shock AS
design [21].
The experiments described herein use the nominal
ignition hohlraum and capsule design described in detail
in Ref. [17]. The hohlraums were 5.75 mm in diameter with
a depleted uranium (DU) wall overcoated with ∼0.5 μm of
Au [39,40]. A 69 1.2 μm thick DT layer was cryogenically frozen on the inner surface of the capsules. The
capsules were CH plastic nominally 1.1 mm in outer radius
and 195 μm thick. The capsules were doped with graded Si
at 1%, 2%, 1% (1 × Si) or 2%, 4%, 2% (2 × Si) at locations
described in Ref. [12] (see Table I). The Si dopant shields
the ice-ablator interface from hard x rays that can preheat
this interface producing an unfavorable Atwood number
leading to increased classical RT growth. However,
increased dopant concentration also steepens the ablation
front density gradient leading to more ablation front
growth. The graded dopant configuration is designed to
optimize these trade-offs [43]. Simulations predict that
2 × Si is more stable to interface growth while more
unstable to ablation front growth. The capsule is supported
inside the hohlraum with a thin membrane or “tent.” The LF
experiments discussed below can be considered nominally
the same with the differences highlighted in Table I. One
notable difference is the AS experiment uses a thinner tent
than the LF implosions which is expected to reduce a seed
for ablation front instability growth [44]. Another notable
difference in the comparison with the HF drive is that the
rate of rise of the main drive is steeper with a 2 ns duration
rather than the 3 ns for the AS and the LF shots discussed
herein. This steeper drive can result in higher velocities and
may also have some RT consequences.
The main differences highlighted in this Letter concern
the laser pulse shapes used to drive the hohlraum. Figure 1
shows three pulse shapes designed to achieve comparable
peak implosion velocity at similar laser energies but with
different fuel α and stability properties [20,21]. The fourshock LF pulse shape was designed to achieve low fuel α
(∼1.5), and on shot N120321 this drive demonstrated the
highest observed ρR [45] and experimental ignition threshold factor [ITFX ¼ ðY=3 × 1015 Þ × ðρR=1.5Þ2.3 ∼ 0.1]
105001-2
PRL 115, 105001 (2015)
TABLE I.
week ending
4 SEPTEMBER 2015
PHYSICAL REVIEW LETTERS
Summary of performance parameters between comparable LF, HF, and AS shots [41,42].
Laser energy [MJ], hohlraum
Pulse
Peak power (Au eq.) [TW]
Rise duration [ns]
Dopant
Capsule tent thickness [nm]
Velocity [km/s]
Total yield [1014 ]
Ti [keV]
DSR [%]
Hot spot radius [μm]
Pτ [atm*s]
N141123
N120311
N120321
N120316
N120417
N120626
N130812
1.60, DU
AS
339 (361)
3
1 × Si
31
320 20
13.67 0.23
3.4 0.15
5.45 0.19
24.8 2.5
16.4 2.1
1.58, DU
LF
334 (359)
3
1 × Si
112
318 20
1.59 0.05
1.95 0.24
4.97 0.3
25.5 3.3
12.5 4.4
1.57, DU
LF
332 (357)
3
2 × Si
110
321 20
5.36 0.18
3.14 0.4
6.24 0.6
24.2 2.6
13.3 3.3
1.56, DU
LF
330 (355)
3
2 × Si þ Ge
110
316 20
2.75 0.08
2.41 0.25
5.8 0.32
25.6 2.5
10.9 2.7
1.67, Au
LF
(355)
3
2 × Si
110
314 20
5.32 0.13
3.05 0.4
5.32 0.2
24.3 1.9
11.6 3.3
1.70, Au
LF
(374)
3
2 × Si
110
314 20
1.18 0.03
1.80 0.14
4.55 0.22
31.5 2.9
7.6 2.0
1.69, Au
HF
(355)
2
1 × Si
44
333 20
27.85 0.59
4.02 0.2
3.96 0.2
36.8 2.6
14.2 1.8
during the NIC [12]. Additionally, N120321 had four
closely related companion shots summarized in Table I.
Shot N130812 utilized the three-shock HF pulse shape,
designed for higher fuel α (2.3–2.7) to improve the stability,
and reduce the convergence ratio [14]. Shot N141123 used
the four-shock AS pulse shape discussed here, designed to
improve the stability properties while maintaining low fuel
adiabat [α ∼ 1.6]. This drive was designed to closely
resemble the five LF companions (see Table I) only with
reduced instability growth via increased energy in the picket.
The power level of the picket was kept the same as the LF to
maintain similar levels of early cross-beam-energy transfer
[46], but with increased picket duration to provide higher
picket drive temperature and initial shock strength [20].
Note that the actual delivered laser energy for N141123 was
8% lower in the picket than requested, which simulations
predict increased the peak growth factor by ∼1.6×. To
account for this, the curves in Fig. 1(b) are from post-shot
calculations for the actual delivered drives. It is also noteworthy that another drive has been designed with slightly
more requested picket energy [23], which is predicted to
result in further reduced growth at comparable adiabat.
The primary and down-scattered neutron images [47]
from the neutron imaging system (NIS) are shown in Fig. 2
for the AS (a), LF (b), and HF (c) implosions. The primary
13–17 MeV neutron contours [48] (red) are formed by DT
FIG. 2 (color online). (a)–(c) Neutron images obtained using
the Neutron Imaging System [47] of (a) AS shot N141123, (b) LF
N120321, and (c) HF N130812.
neutrons escaping from the core, while the down-scattered
contours (black) are lower energy neutrons (6–12 MeV)
resulting from DT neutrons scattering off the stagnated
mass assembly. The NIS images suggest the AS implosion
shows comparable shell shape and size to the LF, while the
hot spot is roughly the same size but more oblate. The HF
implosion N130812 on the other hand, shows a ∼40%
larger shell (consistent with a ∼30% lower ρR) and a strong
toroidal shaped hot spot [15]. The measured yield of
unscattered neutrons is obtained by the activation of Zr
using the flange nuclear activation detectors (FNADs) [49],
which is sensitive to the ΔρR along multiple lines of sight.
The FNADs data for the AS and LF show lower activation
on one or both poles, consistent with increased shell ρR in
these directions. These ρR asymmetries are hypothesized to
be a consequence of polar jets formed by low mode (2–4)
asymmetries [50] from this intrinsic hohlraum-beam geometry and may be further impacted by perturbations from the
tent. These asymmetries are also thought to reduce the
coupling efficiency of the shell to the hot spot [51] and
strongly degrade the yield compared to 1D predictions, an
active area of research where mitigation strategies are
currently being developed.
Figure 3 shows the total neutron yield as a function of
average fuel ρR [12,52–54] for the AS (purple square), LF
(blue), and HF (red) implosions. Also included are all LF
NIC implosions (gray squares) beyond the five companions
in Table I. The AS shot achieved comparable fuel ρR to the
LF, consistent with the comparable in-flight adiabat
inferred from shock velocity measurements [23].
However, the measured neutron yield of the AS implosion
N141123 was considerably higher than all of the LF shots
and 3–10 times higher than the closest companion shots
(blue squares). Also shown is the HF implosion N130812.
Despite the higher total yield of the HF, both the AS and HF
shots lie on contours of ∼1.5× yield amplification due to
the dependence of α-particle self-heating on hot spot ρR,
which is inferred to be higher due to the higher DSR [55]
achieved with the AS drive.
105001-3
PHYSICAL REVIEW LETTERS
PRL 115, 105001 (2015)
Neutron Yield
10
5x
Low−foot
Low−foot 360TW [Au eq.]
High−foot 360TW
Low−foot 360TW AS
16
3x
130812
2x
141123
1.5x
15
10
120321
120417
1.2x
120316
120405
120626 120311
14
10
0.5
0.6
0.7
0.8
0.9 1.0 1.1 1.2
Fuel ρR (g/cm) 2
1.3
1.4
FIG. 3 (color online). Total neutron yield plotted as a function
of fuel ρR for the AS, HF, and LF implosions. The dashed curves
are contours of calculated yield amplification from hot spot alpha
self-heating. The AS achieved significantly higher yield than the
LF platform at comparable ρR.
The measured neutron yield is plotted as a function of the
inferred CH ablator mix mass in the hot spot in Fig. 4(a).
The CH mix mass is inferred from the hard x-ray yield to
neutron yield ratio because of its dependence on hot spot
effective Z [11,12]. This plot shows that for implosions
with inferred CH mix mass >100 ng (the approximate
threshold for detection), the measured yields are low
(<4 × 1014 ). This is likely due to a failure of the integrity
of the DT shell along with increased radiative energy loss
from the injection of higher-Z CH(Si) in the hot spot.
Low−foot
Low−foot 360TW
High−foot 360TW
Low−foot 360TW AS
130812
Neutron Yield
141123
15
10
120321
120417
120316
120311
120405
120626
(b)
120
Low−foot
Low−foot 360TW
High−foot 360TW
Low−foot 360TW AS
100
Hot spot density (g/cc)
(a)
80
120405
141123
60
120311
120417
120316
120626
120321
40
130812
20
14
10
0
200 400 600 800 1000 1200
CH(Si) mix mass (ng)
0
1
2
3
4
5
6
Tion (keV)
FIG. 4 (color online). (a) Total neutron yield plotted as a
function of inferred CH mix mass. (b) Inferred hot spot density as
a function of measured DT ion temperature. Plotted also are
contours of inferred hot spot pressure. AS shot N141123 achieved
considerable hot spot density and pressure compared to the
comparable velocity LF and HF companions.
week ending
4 SEPTEMBER 2015
Figure 4(b) shows the inferred hot spot density as a function
of the inferred ion temperature from the Doppler broadened
DT neutron peak. Apparent in the plot is that the AS shot
achieved higher hot spot temperature than the five comparable LF implosions along with higher hot spot density
than the HF shot. Also included on the plot are contours of
constant hot spot pressure. This high hot spot density and
high temperature results in an inferred hot spot pressure of
P ∼ 150 Gbar for N141123, higher than any implosion
during the NIC.
The performance variability of the low-foot companions
is particularly striking. For example, N120321 holds the
ITFX record during NIC for its combined yield and ρR
[45], while its nearly identical companions (see Table I)
achieved comparable ρR but with a range of observed
yields and temperatures. Of particular note is shot N120311
(the closest companion to N141123 in terms of capsule
dopant and hohlraum), which exhibited particularly low
yield and temperature along with high inferred mix mass.
No difference in initial condition has been identified that
explains why N120311 performed much worse than
N120321. It seems likely that these implosions were all
near shell failure in flight and were especially sensitive to
obscure perturbation sources such as the tent [44] or
possible absorption of oxygen by the ablator [56]. The
significantly lower yield of N120311 compared to the AS is
related to the low observed Ti (∼40%), a likely consequence of the high observed CH mix and accompanying
radiative losses. Interestingly, the HF implosion achieved
∼2X higher yield than the AS, but with reduced ρR [15],
due to the higher adiabat. The increased yield is consistent
with the 18% higher Ti. The picture that the LF design was
near breakup is further supported by the fact that when the
N120321-LF design was pushed to higher power (387 TW)
and energy on shot N120405 (labeled gray point on
Figs. 3 and 4), the performance was poor with a yield
1.6 × 1014 and with ∼600 ng of CH mix into the hot spot. It
is also noteworthy that the reduction of the ablation front
growth on N141123 results in improved yield over LF
implosions for which the inferred mix mass [Fig. 4(a)] was
negligible, like N120321 and N120417 [45]. This suggests
that even without mix of CH-ablator material into the hot
spot, the feedthrough of ablation front growth to the hot
spot boundary causes significant perturbation to the burning DT volume. This may also indicate that implosions
during the NIC were significantly perturbed by ablation
front growth even when the inferred CH mix was low or
even negligible.
In summary, an “adiabat-shaped” indirect drive implosion designed to reduce ablation front growth and achieve
high ρR has resulted in markedly improved performance
when compared to the low-foot implosions during the NIC.
This improvement suggests a dominant role of growth
during the acceleration phase of the implosion in degrading
implosion performance via reduced hot spot volume and
105001-4
PRL 115, 105001 (2015)
PHYSICAL REVIEW LETTERS
increased radiation losses from the mix of CH into the hot
spot during the NIC. Recent results have shown that the tent
perturbation [44], surface roughness, and other seeds
internal to the plastic [56] are more severe than originally
expected in ignition designs and have increased the relative
role of the ablation front growth for implosions during the
NIC. However, this result shows that these perturbations
can be partly controlled using only the laser pulse shape
while simultaneously achieving a high compression of
ρR > 1 g=cm2 . This represents an important step forward
in managing the stability tradeoffs of achieving high
velocity and high ρR, both necessary requirements for
ignition.
The authors sincerely thank the NIF operations staff who
supported this work. We gratefully acknowledge helpful
conversations with O. Hurricane, J. Lindl, and J. Perkins.
This work was performed under the auspices of the U.S.
Department of Energy by Lawrence Livermore National
Laboratory under Contract No. DE-AC52-07NA27344.
[1] E. I. Moses, J. Phys. Conf. Ser. 112, 012003 (2008).
[2] J. D. Lindl, P. Amendt, R. L. Berger, S. G. Glendinning,
S. H. Glenzer, S. W. Haan, R. L. Kauffman, O. L. Landen,
and L. J. Suter, Phys. Plasmas 11, 339 (2004).
[3] S. Atzeni and J. Meyer-ter-Vehn, The Physics of Inertial
Fusion, International Series of Monographs on Physics
(Oxford University Press, Oxford, 2004).
[4] J. P. Freidberg, Plasma Physics and Fusion Energy
(Cambridge University Press, Cambridge, England, 2007).
[5] R. Betti, P. Y. Chang, B. K. Spears, K. S. Anderson, J.
Edwards, M. Fatenejad, J. D. Lindl, R. L. McCrory, R. Nora,
and D. Shvarts, Phys. Plasmas 17, 058102 (2010).
[6] L. Rayleigh, Scientific Papers II (Cambridge University
Press, Cambridge, England, 1900), p. 200.
[7] G. Taylor, Proc. R. Soc. A 201, 192 (1950).
[8] R. Betti, V. N. Goncharov, R. L. McCrory, and C. P. Verdon,
Phys. Plasmas 5, 1446 (1998).
[9] A. J. Mackinnon et al., Phys. Rev. Lett. 108, 215005 (2012).
[10] S. P. Regan et al., Phys. Rev. Lett. 111, 045001 (2013).
[11] T. Ma et al., Phys. Rev. Lett. 111, 085004 (2013).
[12] M. J. Edwards et al., Phys. Plasmas 20, 070501 (2013).
[13] J. Lindl, O. Landen, J. Edwards, E. Moses, and N. Team,
Phys. Plasmas 21, 020501 (2014).
[14] T. R. Dittrich et al., Phys. Rev. Lett. 112, 055002 (2014).
[15] H. S. Park et al., Phys. Rev. Lett. 112, 055001 (2014).
[16] O. A. Hurricane et al., Nature (London) 506, 343 (2014).
[17] S. W. Haan et al., Phys. Plasmas 18, 051001 (2011).
[18] D. T. Casey et al., Phys. Rev. E 90, 011102 (2014).
[19] S. G. Glendinning et al., Phys. Plasmas 7, 2033 (2000).
[20] J. Milovich et al. preparation (to be published).
[21] D. S. Clark et al., Phys. Plasmas 21, 112705 (2014).
[22] M. M. Marinak, G. D. Kerbel, N. A. Gentile, O. Jones, D.
Munro, S. Pollaine, T. R. Dittrich, and S. W. Haan, Phys.
Plasmas 8, 2275 (2001).
[23] K. L. Baker et al., Phys. Plasmas 22, 052702 (2015).
[24] K. O. Mikaelian, Phys. Rev. A 42, 3400 (1990).
week ending
4 SEPTEMBER 2015
[25] A. L. Velikovich, F. L. Cochran, and J. Davis, Phys. Rev.
Lett. 77, 853 (1996).
[26] N. Metzler, A. L. Velikovich, and J. H. Gardner, Phys.
Plasmas 6, 3283 (1999).
[27] K. Anderson and R. Betti, Phys. Plasmas 10, 4448 (2003).
[28] R. Betti, K. Anderson, J. Knauer, T. J. B. Collins, R. L.
McCrory, P. W. McKenty, and S. Skupsky, Phys. Plasmas
12, 042703 (2005).
[29] V. N. Goncharov, J. P. Knauer, P. W. McKenty, P. B. Radha,
T. C. Sangster, S. Skupsky, R. Betti, R. L. McCrory, and
D. D. Meyerhofer, Phys. Plasmas 10, 1906 (2003).
[30] J. P. Knauer et al., Phys. Plasmas 12, 056306 (2005).
[31] V. A. Smalyuk, V. N. Goncharov, K. S. Anderson, R. Betti,
R. S. Craxton, J. A. Delettrez, D. D. Meyerhofer, S. P. Regan,
and T. C. Sangster, Phys. Plasmas 14, 032702 (2007).
[32] R. D. Richtmyer, Commun. Pure Applied Math.13, 297 (1960).
[33] E. E. Meshkov, Izv. Acad. Sci. USSR Fluid Dyn. 4, 101
(1969).
[34] V. N. Goncharov, Phys. Rev. Lett. 82, 2091 (1999).
[35] J. L. Peterson, D. S. Clark, L. P. Masse, and L. J. Suter,
Phys. Plasmas 21, 092710 (2014).
[36] A. G. MacPhee et al. (to be published).
[37] J. L. Peterson, L. F. Berzak Hopkins, O. S. Jones, and D. S.
Clark, Phys. Rev. E 91, 031101 (2015).
[38] V. Smalyuk et al. (to be published).
[39] Note in some experiments with the LF, and HF pulses, a Au
hohlraum with an additional 25 TW peak power was used to
obtain a similar radiation drive, and, therefore, similar peak
implosion velocities as DU (see Table I).
[40] T. Döppner et al., Phys. Rev. Lett. 115, 055001 (2015).
[41] Note here the hot spot radius is the effective radius inferred
from the reconstructed x-ray volume.
[42] Note the values of P τ are inferred from experimental data
which are effected by alpha heating, while the motivating
discussion in the introduction neglected alpha heating.
[43] D. S. Clark, S. W. Haan, B. A. Hammel, J. D. Salmonson,
D. A. Callahan, and R. P. J. Town, Phys. Plasmas 17,
052703 (2010).
[44] S. R. Nagel et al., Phys. Plasmas 22, 022704 (2015).
[45] V. A. Smalyuk et al., Phys. Rev. Lett. 111, 215001 (2013).
[46] P. Michel, W. Rozmus, E. A. Williams, L. Divol, R. L.
Berger, S. H. Glenzer, and D. A. Callahan, Phys. Plasmas
20, 056308 (2013).
[47] G. P. Grim et al., Phys. Plasmas 20, 056320 (2013).
[48] The outer contour is 17% of the peak with each inward contour
increasing by integer multiples (17%, 34%, 51%, etc.).
[49] D. L. Bleuel et al., Rev. Sci. Instrum. 83, 10D313 (2012).
[50] J. R. Rygg et al., Phys. Rev. Lett. 112, 195001 (2014).
[51] A. L. Kritcher et al., Phys. Plasmas 21 (2014).
[52] Note that here ρR is approximated from the measured
neutron down-scattered ratio (DSR) where fuel
ρR½g=cm2 ∼ 0.19 × DSR [%] and total yield is inferred
as Y tot ∼ Y 13−15 e4.0DSR , where Y 13−15 is the integrated
neutron yield from 13–15 MeV.
[53] M. G. Johnson et al., Rev. Sci. Instrum. 83, 10D308 (2012).
[54] J. A. Frenje et al., Nucl. Fusion 53, 043014 (2013).
[55] P. Patel et al., Bull. Am. Phys. Soc. 58, 4.00001 (2013).
[56] S. W. Haan, H. Huang, M. A. Johnson, M. Stadermann,
S. Baxamusa, S. Bhandarkar, D. S. Clark, V. Smalyuk, and
H. F. Robey, Phys. Plasmas 22, 032708 (2015).
105001-5